Feed-forward chains of recurrent attractor neural networks with finite dilution near saturation |
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| Institution: | 1. Polytechnic Institute of Leiria, School of Health Sciences (ESSLei – IPL), Department of Health Technologies, Campus 2 - Morro do Lena – Alto do Vieiro, 2411-901 Leiria, Portugal;2. School of Health Sciences of the University of Aveiro (ESSUA), Campus Universitário de Santiago, Agras do Crasto, Edifício 30, 3810-193 Aveiro, Portugal;1. Department of Neurology, University Medical Center Göttingen, Göttingen, Germany;2. Department of Ophthalmology, University Medical Center Mainz, Experimental and Translational Ophthalmology, Mainz, Germany;3. Department of Medical Statistics, University Göttingen, Facility for Medical Biometry and Statistical Bioinformatics, Göttingen, Germany;4. Deutsche Forschungsgemeinschaft - German Research Center for Nanoscale Microscopy and Molecular Physiology of the Brain, Göttingen, Germany;5. Klinikum Rechts der Isar der Technischen Universität München, Munich, Germany;1. Department of Human Neurosciences, “Sapienza” University of Rome, V.le delle Università 30, 00185, Rome, Italy;2. Department of Anatomic, Histologic, Forensic Medicine and Orthopedics Sciences, “Sapienza” University of Rome, via A. Borelli 50, 00161, Rome, Italy;3. IRCCS NEUROMED, Via Atinense 18, 86077, Pozzilli, IS, Italy;1. Multimodal Neuroimaging Group, Department of Nuclear Medicine, Faculty of Medicine and University Hospital of Cologne, University of Cologne, Germany;2. Institute of Medical Science and Technology, Shahid Beheshti University, Tehran, Iran;3. Institute of Neuroscience and Medicine (INM-7), Research Center Jülich, Germany;4. Institute for Systems Neuroscience, Heinrich-Heine University Düsseldorf, Germany;5. Department of Neurology, Faculty of Medicine and University Hospital of Cologne, University of Cologne, Germany;6. German Center for Neurodegenerative Diseases (DZNE), Bonn-Cologne, Germany |
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| Abstract: | A stationary state replica analysis for a dual neural network model that interpolates between a fully recurrent symmetric attractor network and a strictly feed-forward layered network, studied by Coolen and Viana, is extended in this work to account for finite dilution of the recurrent Hebbian interactions between binary Ising units within each layer. Gradual dilution is found to suppress part of the phase transitions that arise from the competition between recurrent and feed-forward operation modes of the network. Despite that, a long chain of layers still exhibits a relatively good performance under finite dilution for a balanced ratio between inter-layer and intra-layer interactions. |
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